problem set 3

# problem set 3 - Problem Set #3 Suspending a Speaker A...

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Problem Set #3 Suspending a Speaker A loudspeaker of mass 15.0 is suspended a distance of = 2.20 below the ceiling by two cables that make equal angles with the ceiling. Each cable has a length of = 2.90 . Part A What is the tension in each of the cables? Hint A.1 How to approach the problem We know that and , the tension forces, are directed along their respective cables. Since the loudspeaker is in equilibrium, the vector sum of and must exactly balance any other forces that act on the loudspeaker. Since the two cables are at equal angles, there is no reason for the magnitudes of the tensions in the cables to differ. The tensions in the two cables are in fact the same. Therefore, both of them can be called . Then, using , where is the angle between a cable and the ceiling, solve for the value of . Hint A.2 Identify the forces Besides the forces of tension, what forces act on the loudspeaker? ANSWER: weight only the normal force only weight and the normal force Correct

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Hint A.3 Find the net vertical force What is , the sum of the vertical components of the tensions in the two cables? Recall that the sum of all forces acting in the vertical direction must equal zero, or else the speaker would accelerate up or down. Use 9.80 for the magnitude of the acceleration due to gravity. ANSWER: = 147 Correct Hint A.4 Determine You know that the vertical component of the tension in one of the cables is equal to , where is the angle that the cable makes with the ceiling, as shown in the figure. What is ? Hint A.4.1 Using the property of the right triangle Recall that you are given the length of the cable (indicated by in the figure) and the distance from the ceiling at which the speaker is suspended (indicated by in the figure). Also, note that in a right triangle one leg is equal to the sine of the opposite angle times the hypotenuse. Express your answer numerically. ANSWER: = 0.759 Correct Use 9.80 for the magnitude of the acceleration due to gravity. ANSWER: = 96.9 Correct Conical Pendulum I
is suspended from a fixed point with a massless string of length (i.e., it is a pendulum). You are to investigate the motion in which the string moves in a cone with half-angle . Part A What tangential speed, , must the bob have so that it moves in a horizontal circle with the string always making an angle from the vertical? Hint A.1 What's happening here? Hint not displayed Hint A.2 Find the vertical acceleration of the bob Hint not displayed Hint A.3 Find the tension in the string Hint not displayed Hint A.4 Find the horizontal acceleration of the bob Hint not displayed Hint A.5 Find the horizontal force Hint not displayed Express your answer in terms of some or all of the variables , , and , as well as the acceleration due to gravity . ANSWER:

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## This note was uploaded on 04/07/2010 for the course PHYS 3163 taught by Professor Pickett during the Spring '10 term at CSU Long Beach.

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problem set 3 - Problem Set #3 Suspending a Speaker A...

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